You have to learn about nitrogen cycle, so it's good that you take your time before introducing fishs.
For the heater, it's always good to have one, as it prevents temps swings. No need for a heater for cold water fishs.
For a 10g, you can put some nano hardy fishs... You can go with only one betta too, but if something is wrong with the water, the betta won't tell you and will still thrive... Maybe shrimps or snails or ampullar interest you ?
Can you tell us the parameters of your water ? You can go to your LFS if you don't want to invest in a water test kit. We need to know the KH and GH of your tap... Maybe the PH of tap water sitting in a glass for 24 hours can be great too... You just bring a bottle of water to the LFS and they'll test GH KH.
Platies are great for 10g too... To begin you'll really want hardy species... Or maybe you want to go for some more delicates species like tetras...
You'll learn faster with tetra, you know when they're not happy. They swim everywhere/hide if not happy, or simply dies. One day you'll wash all your filter media under tap, and one week after you'll find your fishs dead, so you'll learn from this mistake -.-
Here's what you need: 10-20g filter, 10g tank, cheap light (timer if you want), heater (optionnal except for tropical species), substrate (go with something that look natural, you'll become bored over time of a pink or blue substrate), decorations or hiding places for your fishs, airpump is a great accessory but optionnal...
You'll need some products... I suggest you take dechlorinator (nutrafin aqua+) BB in bottle (Nutrafin Cycle)... You'll need food flake of frozen depending on the species you choose